Graph f^-1(f)=f/x

Find where the expression ${\displaystyle \frac{f}{x}}$ is undefined.

The vertical asymptotes occur at areas of infinite discontinuity.

Consider the rational function ${\displaystyle R\left(x\right)=\frac{a{x}^n}{b{x}^m}}$ where ${\displaystyle n}$ is the degree of the numerator and ${\displaystyle m}$ is the degree of the denominator.

Find ${\displaystyle n}$ and ${\displaystyle m}$.

Since ${\displaystyle n<m}$, the x-axis, ${\displaystyle y=0}$, is the horizontal asymptote.

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

This is the set of all asymptotes.